The Supreme Court has denied a request by Hobby Lobby to shield the company from the so-called contraceptive mandate while its legal battle plays out, after a federal court last week similarly ruled against the Christian-owned company.

The lower court had earlier refused to protect the company from an ObamaCare-tied requirement to provide contraceptive coverage, and the fines that come with it for not complying.

CEO David Green, who had taken his case to the appeals court after losing in a lower-court ruling, had argued that his family would have to either "violate their faith by covering abortion-causing drugs or be exposed to severe penalties."

The Supreme Court's latest ruling is not on the underlying merits of the mandate itself -- it simply denies the company's request for an injunction while legal battle on the merits plays out. There are currently more than 40 cases pending against that rule.

The mandate requires businesses and organizations, with some exceptions, to provide access to contraception coverage -- Hobby Lobby was most concerned about coverage for the morning-after pill, which some consider tantamount to an abortion-causing drug. Hobby Lobby has refused to comply, while saying the fines could add up to $1.3 million a day.

In its earlier ruling, the 10th Circuit Court of Appeals said the company did not prove the rule would "substantially burden" its religious freedom. Though the mandate has exemptions for religious entities like churches, the lower court ruled that Hobby Lobby is not a religious group.

The company, founded in 1972, has more than 13,000 full-time employees across more than 500 stores.